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AN INFINITE-DIMENSIONAL WEAK KAM THEORY VIA RANDOM VARIABLES
Journal article   Open access  Peer reviewed

AN INFINITE-DIMENSIONAL WEAK KAM THEORY VIA RANDOM VARIABLES

Diogo Gomes and Levon Nurbekyan
Discrete and continuous dynamical systems. Series A, Vol.36(11), pp.6167-6185
01/11/2016
DOI: https://doi.org/10.3934/dcds.2016069

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
We develop several aspects of the in finite-dimensional Weak KAM theory using a random variables' approach. We prove that the in finite-dimensional cell problem admits a viscosity solution that is a fixed point of the Lax-Oleinik semigroup. Furthermore, we show the existence of invariant minimizing measures and calibrated curves defined on R.
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https://doi.org/10.3934/dcds.2016069View
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